. Which is the better investment?
a. $1,200 at 9% simple interest for 2 years
b. $1,200 at 8% compound interest for 2 years

The p-value for this z test statistic is equal to 0.0287.

A null hypothesis (H₀) can be defined the opposite of an alternate hypothesis (H₁) and it asserts that two (2) possibilities are the same.

The z test statistic can be calculated by using this formula:

[tex]t=\frac{x\;-\;u}{\frac{\delta}{\sqrt{n} } }[/tex]

Where:

In this scenario, the z test statistic for a one-tailed hypothesis test (lower tail) is equal to -1.9. Therefore, by using a t-distribution and z-score calculator for a normal distribution, the p-value for this test is given by:

P-value = P(t > -1.9)

P-value = 0.0287.

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The mean sleep time is 16.54 hours per day for newborn babies

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The mean sleep time is 16.54 hours per day for newborn babies.

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The number of balcony seats sold is 110

Finding Unknown quantity using Linear equation:

The linear equation is an equation that is used to find an unknown quantity or an unknown number. In this, we will represent the Uknown value with a variable like x, y, z, etc.  

Here we have

Tickets for a community theater cost $11 for each main-floor seat
and $6 for each balcony seat.

There are 400 seats on the main floor, which are sold out for the evening performance  

The total revenue from ticket sales was $5060.

Here we don't know the number of balcony seats.

Let us assume that number of balcony seats = x

Then total revenue = 400(11) + 6x = 5060

=> 4400 + 6x = 5060

=> 6x = 5060 - 4400

=> 6x = 660

=> x = 110  

Therefore,

The number of balcony seats sold = 110

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Answer:

surface area=2(lb+lh+bh)

surface area=2(9)(4)+(9)(12)+(4)(12)

surface area=384cm2

Using a 98% confidence interval, the total number of customers that should be sampled is 87.

The sample size refers to the number of observations in the data set, and as the sample size increases, the calculated value of population parameters becomes more reliable and true. In other words, as sample size increases, the value of the margin of error decreases.

Given,

Standard deviation σ=300

Confidence level: 0.98

Maximum allowable error: ε=75

The critical value is calculated using the standard normal table at the level of significance (0.02)

The critical value in this case is 2.326.

Sample size is calculated by,

n=((Z[tex]z_{\alpha /2}[/tex])²×σ²))/ε²

n=((2.326)²×(300)²)/(75)²

n=86.564≈87

Therefore, the required sample size is 87.

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The required value of h is 5.29 ft in the parallelogram shown.

A parallelogram is defined as a special type of quadrilateral that has both pairs of opposite sides parallel and equal.

As per the given figure, the dotted lines create a triangle, and the hypotenuse of that triangle is the opposite base of the parallelogram, indicating that it is likewise 8 feet long.

The base of the newly made triangle is one of the parallelogram's diagonals, which is 6 feet long.

According to Pythagorean's theorem, we have

h² + 6² = 8²

h² + 36 = 64

h² = 28

h = √28

h = 5.29

Thus, the required value of h is 5.29 ft.

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Answer:

4

I did the i-ready, hope this helps! :)

Answer:

-6

Step-by-step explanation:

The value of [tex]b[/tex] is the same as the value of [tex]y[/tex] when [tex]x=0[/tex].

Answer:

= (2x + 5y) * (2x - 5y)

Step-by-step explanation:

4x²-25y²
= (2x)² - (5y)²
= (2x + 5y) * (2x - 5y)

Answer:

[tex]\huge\boxed{\sf (2x + 5y)(2x - 5y)}[/tex]

Step-by-step explanation:

[tex]4x^2-25y^2[/tex]

Both of the terms are perfect squares.

[tex](2x)^2-(5y)^2[/tex]

= (2x + 5y)(2x - 5y)

[tex]\rule[225]{225}{2}[/tex]

Exactly one type of meat required = 5 choices

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The derivative of the given polynomial equation is 16x³ - 6x + 6.

We are given an equation. The equation represents a polynomial in one variable. The degree of the polynomial is four; hence, it is called biquadratic. We need to find the derivative of the given polynomial. The derivative of a function of a real variable in mathematics describes the sensitivity of the function value to a change in its argument. Calculus relies heavily on derivatives.

The equation is given below.

y = 4x^4 - 3x² + 6x + 14

dy/dx = (d/dx)(4x^4 - 3x² + 6x + 14)

dy/dx = (d/dx)(4x^4) - (d/dx)(3x²) + (d/dx)(6x) + (d/dx)(14)

dy/dx = [4*4x^(4 - 1)] - [3*2x^(2 - 1)] + [6*1x^(1 - 0)] + [14*0x^(0 - 1)]

dy/dx = 16x³ - 6x + 6

Hence, the derivative of the given polynomial equation is 16x³ - 6x + 6.

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The histogram that shows a left-skewed distribution is given by:

A. A bar chart plots data points (1, 1), (2, 4), (3, 1), (4, 2), (5, 3), (6, 4) and (7, 3).

An histogram is a graph that shows the number of times each element x was observed on the data-set.

Hence, the meaning of a point (x,y) on the histogram is given as follows:

Observation x was observed y times on the data-set.

The skewness of a distribution can be explained as follows:

Hence in this problem, for the left-skewed histogram, we want an "increasing" histogram, hence option A is correct.

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The two triangles are congruent by SAS criterion.

Verification:

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Answer: I would say non linear. I have done problems like these before and anytime there is an exponent in the equation it always ends up being non linear. Also remember for it to be linear it most form a straight line that passes through the origin.

Step-by-step explanation:

The factor of the polynomial f(x) graphed on the coordinate plane is

(x - 1).

What is factor of the polynomial?

A polynomial with coefficients in a certain field or in integers is expressed as the product of irreducible factors with coefficients in the same domain in mathematics and computer algebra, which is known as polynomial factorization.

A polynomial can be factored by expressing it as the product of two or more components; this is somewhat the opposite of multiplying.

From the given graph we can see that, graph crosses x - axis at points

x = 1 and x = 8.

That means x = 1, 8 are the zero of the polynomial.

Since, if x = a is a zero of the polynomial, then (x - a) is the factor of the polynomial.

As x = 1, 8 are zero of the polynomial so (x - 1) and (x - 8) are the factors of the polynomial.

Hence, from the given options (x - 1) is factor of the polynomial.

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The required value of a₄ is 10,202 to the given recursive formula.

An arithmetic sequence is defined as an arrangement of numbers that is in a particular order.

The given recursive formula in the question as:

aₙ = (aₙ ₋₁ )² + 1 ....(i)

And, a₁ = 3

Substitute the value of a₁ = 3 in equation (i), and solve for n = 2

a₂ = (a₁)² + 1

a₂ = (3)² + 1

a₂ = 9 + 1 = 10

Substitute the value of a₂ = 10 in equation (i), and solve for n = 3

a₃ = (10)² + 1

a₃ = 100 + 1 = 101

Substitute the value of a₃ = 101 in equation (i), and solve for n = 4

a₄ = (101)² + 1

a₄ = 10,201 + 1

a₄ = 10,202

Therefore, the required value of a₄ is 10,202.

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Answer:

(0, 6)

Step-by-step explanation:

Given function:

[tex]y=\log_4(2x+64)+3[/tex]

The y-intercept of a function is the point at which the curve crosses the y-axis, so when x = 0.

Therefore, to find the y-intercept, substitute x = 0 into the function:

[tex]\implies y=\log_4(2(0)+64)+3[/tex]

[tex]\implies y=\log_4(64)+3[/tex]

Rewrite 64 as 4³:

[tex]\implies y=\log_4(4)^3+3[/tex]

[tex]\textsf{Apply the log power law}: \quad \log_ax^n=n\log_ax[/tex]

[tex]\implies y=3\log_4(4)+3[/tex]

[tex]\textsf{Apply log law}: \quad \log_aa=1[/tex]

[tex]\implies y=3(1)+3[/tex]

[tex]\implies y=3+3[/tex]

[tex]\implies y=6[/tex]

Therefore, the y-intercept of the given function is (0, 6).

Step-by-step explanation:

one side.

as each tile is guaranteed an equilateral triangle, all sides are equally long. measuring 1 side clarifies therefore the overall size of the tile.

the angles are the same in any case, as every equilateral triangle (no matter its size) has only angles of 60°.

so, if any side has the same length as the side lengths of the other triangles, then the checked triangle is congruent with the others.

The statement "The median and altitude of an isosceles triangle can be same", is verified by drawing diagram

The statement is  

"The median and altitude of an isosceles triangle can be same"

Draw an isosceles triangle ABC with BD = CD,

Draw a line segment AD perpendicular to the side BD

Here AD is the height of the triangle which is the altitude of the triangle

From the figure we can see that the length of BD = length of CD

Where D is the mid point of the line BD.

Therefore the line AD is the median of the triangle

Hence, The statement "The median and altitude of an isosceles triangle can be same", is verified by drawing diagram

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Answer:

(15-3x³) is the answer.

Step-by-step explanation:

2*15-2*3x³

which is 30-6x³.

Using the Pythagorean Theorem and the given values, we can solve for c.

a^2 + b^2 = c^2
12^2 + 16^2 = c^2
144 + 256 = c^2
400 = c^2
√400 = √c^2
c = 20

the slop is -1 and the y-intercept is (0,7)

acc to our question-

Hence,the slop is -1 and the y-intercept is (0,7)

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Answer:

y+6 =-2(x-5)

Step-by-step explanation:

The question is asking for the equation of the line

The equation for point-slope form is always written as y-y₁=m(x-x₁)

y₁ and x₁ are the points given to you in this order (x₁, y₁)

so x₁=5 and y₁=-6

Now you plug in all the numbers you have into the point slope form

y- (-6)= -2(x-5)

When you subtract a negative (a double negative you get a positive)

y+6=-2(x-5)

Point-Slope form is usually the easiest form of a line to write since you do not need to solve for any intercepts or other points. You have y on one side of the equation, usually the left to make it easier to read, and x on the other, usually the right.You subtract the point that you are given from the y and the x. Multiply everything that is on the same side of the equation of the x by the slope (m).

Notes:

For y₁ and x₁, they could be any point on the line. For example, (1,2) is also on this line. So the equation would be

y-2=-2(x-1)

[tex]a=-5(-3)-2=13\\\\b=-5(-1)-2=3\\\\c=-5(1)-2=-7\\\\d=-5(2)-2=-12[/tex]

Answer:

A = 13 B = 3 C = -7 D = -12

Step-by-step explanation:

Just insert the x values for a, b, c, and d. for example if we were to find a.

The x value for a is -3 so we would put -3 in place of x in the equation.

-5(-3) - 2

Remember: Two negative numbers multiplied with each other equal a positive.

15 - 2 = 13

Using the concepts of hypothesis test, we got that something is happening that wasn’t accounted for as a result when a significant chi-square value is obtained.

A chi-squared test (symbolically represented as χ2) is basically the data analysis on the basis of the observations of a random set of variables. Usually, it is the comparison of two statistical data sets. This test was introduced by Karl Pearson in the 1900 for categorical data analysis and distribution. So it was mentioned as a Pearson’s chi-squared test.

The chi-square test is actually used to estimate how likely the observations that are made would be, by considering assumption of the null hypothesis as true.

Hence, a study is designed to test whether there is a relationship between natural hair colors and eye colors, in that case if a significant chi-square value is obtained it suggests that something is happening that wasn’t accounted for .

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Answer:

Step-by-step explanation:

Distance equation:

If cars move in opposite directions their speeds add up, then the distance between them after 1.5 hours is:

Answer:

After 1.5 hr, they are 3s - 7.5 mi away.

Step-by-step explanation:

Forming the expression,

→ 1.5 × (s + s - 5)

Now the required solution will be,

→ 1.5 × (s + s - 5)

→ 1.5 × (2s - 5)

→ 1.5(2s - 5)

→ 3s - 7.5

Hence, answer is 3s - 7.5 miles.

The culture starts out with 39 members.

Given that;

After 20 minutes and 40 minutes, a bacteria culture had an 800 and 1700 count, respectively.

To get exponential growth;

We can get growth with an exponential function,

F(t) = A₀[tex]e^k^t[/tex]

Here, k is the growth constant and A₀ is the initial amount of bacteria.

Let;

800 = A₀[tex]e^2^0^k[/tex]  → (I)

1700 = A₀[tex]e^4^0^k[/tex] → (II)

From (I) and (II);

1700 / 800 =  A₀[tex]e^4^0^k[/tex] / A₀[tex]e^2^0^k[/tex]

17/8 = [tex]e^2^0^k[/tex]

For the above equation take the natural log on both sides;

ln(17/8) = ln [tex]e^2^0^k[/tex]

ln(17/8) = 20k

k = ln(17/8) / 20

To get the initial size of the culture;

From (I),

800 = A₀[tex]e^2^0^k[/tex]

800 = A₀e⁰°⁰³⁷⁶ ˣ ²⁰

A₀ = 800 / 20.76

A₀ = 38.53 ≅ 39

Therefore, the initial size of the culture is 39.

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